Infinite lotteries, large and small sets

Synthese 194 (6):2203-2209 (2017)
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Abstract

One result of this note is about the nonconstructivity of countably infinite lotteries: even if we impose very weak conditions on the assignment of probabilities to subsets of natural numbers we cannot prove the existence of such assignments constructively, i.e., without something such as the axiom of choice. This is a corollary to a more general theorem about large-small filters, a concept that extends the concept of free ultrafilters. The main theorem is that proving the existence of large-small filters requires a nonconstructive axiom like AC.

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Citations of this work

Might All Infinities Be the Same Size?Alexander R. Pruss - 2020 - Australasian Journal of Philosophy 98 (3):604-617.

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References found in this work

What conditional probability could not be.Alan Hájek - 2003 - Synthese 137 (3):273--323.
Regularity and Hyperreal Credences.Kenny Easwaran - 2014 - Philosophical Review 123 (1):1-41.
Fair infinite lotteries.Sylvia Wenmackers & Leon Horsten - 2013 - Synthese 190 (1):37-61.
Happy families.A. R. D. Mathias - 1977 - Annals of Mathematical Logic 12 (1):59.

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